Existence of maximizers for Sobolev–Strichartz inequalities

We prove the existence of maximizers of Sobolev–Strichartz estimates for a general class of propagators, involving relevant examples, as for instance the wave, Dirac and the hyperbolic Schrödinger flows.     

Syntheses,structure, and reactivity of acyclic enetriyne and enetetrayne derivatives

Sonogashira coupling of buta-1,3-diynylbenzene with ((2-iodophenyl)ethynyl)trimethylsilane and 1,2-diiodobenzene led to the novel enetriyne, 1-ethynyl-2-(phenylbuta-1,3-diynyl)benzene, and enetetrayne, 1,2-bis(phenylbuta-1,3-diynyl)benzene, respectively. Solid state structural and thermal analyses are also described. In solution, 1-ethynyl-2-(phenylbuta-1,3-diynyl)benzene was found to undergo thermal Bergman cyclization to afford 2-(phenylethynyl)naphthalene.     

On circular–linear one-factorizations of the complete graph

In Korchmáros et al. (2018)one-factorizations of the complete graph $K_n$ are constructed for $n=q+1$ with any odd prime power $q$ such that either $q\equiv 1(mod4)$ or $q=2^h?1$. The arithmetic restriction $n=q+1$ is due to the fact that the vertices of $K_n$ in the construction are the points of a conic $\Omega$ in the finite plane of order $q$. Here we work on the Euclidean plane and describe an analogous construction where the role of $\Omega$ is taken by a regular $n$-gon. This allows us to remove the above constraints and construct one-factorizations of $K_n$ for every even $n\ge 6$.     

Exploring the Phase-Selective,Green, Hydrothermal Synthesis of Upconverting Doped Sodium Yttrium Fluoride: Effects of Temperature,Time, and Precursors

The aim of this work was i) to develop a hydrothermal, low-temperature synthesis protocol affording the upconverting hexagonal phase NaYF₄ with suitable dopants while adhering to the “green chemistry” standards and ii) to explore the effect that different parameters have on the products. In optimizing the synthesis protocol, short reaction times and low temperatures (below 150 °C) were considered. Yb³⁺ and Er³⁺ ions were chosen as dopants for the NaYF₄ material. Within the context of the second goal, parameters including nature of the precursors, treatment temperature, and treatment time were investigated to afford a pure hexagonal crystalline phase, both in the doped and undoped materials. To fully explore the synthesis results, the prepared materials were characterized from a structural (XRD), compositional (XPS, ICP-MS), and morphological (SEM) point of view. The upconverting properties of the compounds were confirmed by photoluminescence measurements.